Aptitude - Problems on H.C.F and L.C.M - Discussion

Read the question clearly.

Given that the two factors is 13 and 14 this means 23 is also a factor of L.C.M.

So LCM is 23*13*14.

Now 23 is HCF so suppose two numbers are 23*x and 23*y.

By theorem; (23*x)(23*y) = (23)(23*13*14).

This gives x equal to either 13 or 14 and similarly y.

Very good explanations.

LCM*HCF = Value of that number.

So, HCF(LCM1) = n1.

HCF*LCM2 = n2.

So 23*13 = n1.

23*14 = n2.

N1<N2.

HCF means highest common factor.

LCM means least common Multiple.

Both are different. In this question they have given HCF of two numbers are 23.

Let us consider x and y as two no's then HCF (x, y) = 23.

We don't know the value of x and y. Then LCM of the two nos have factors 13 and 14.

This means that LCM (x, y) = z.

The value z have factors 13 and 14 which will divide z without leaving a remainder.

The main question is finding the larger of the two no is? That means we have to find biggest value among x and y.

I have understood the question but I don't how to solve it. I need clear explanation please.

Answer which is explained above assumes that the extra factors 13 and 14 are included in two separate numbers. The question does not say anything of this sort.

So technically, the correct answer is n1 = 23 and n2 = 23 x 13 x 14 = 4186.

You can verify that HCF = 23 and LCM = 2 x 7 x 13 x 23 = (2 x 7) x 13 x 23, for which the given statement that "The other two factors included in the LCM are 13 and 14" is perfectly valid.

Please clear the concept easily.

I'm little bit confuse in this concept. How we know to solve this ways. Please anybody is there to clear my doubt.

Dear Friends,

Still I didn't understand the concept of LCM & HCF.

Please explain me in an easy way.

I am confused with the question and method of solution. Can anyone help me?

We have the terms HCF, LCM, product of 2 numbers (numbers be a,b).

In general,
Number = Factor * Factor.

eg :
6= 2*3 ----> 2, 3 factors of number 6.
8= 2*4-----> 2, 4 factors of 8.

So,
a = Factor * Factor.
b = Factor * Factor.

Here the 2 factors are 13, 14.

Given that, the highest common factor is 23,
So, we got another factor 23.

We require 4 factors to get a & b. But we have only 3.
And clearly said 23 is highest common factor.

Where 23 is a common factor in both a & b.

a = 23 * 13.
b = 23 * 14.

Therefore, the larger number = (23 x 14) = 322.

Hope you all understand this, if any mistake correct me.